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A354561
Numbers divisible by the cube of their largest prime factor.
2
8, 16, 27, 32, 54, 64, 81, 108, 125, 128, 162, 216, 243, 250, 256, 324, 343, 375, 432, 486, 500, 512, 625, 648, 686, 729, 750, 864, 972, 1000, 1024, 1029, 1125, 1250, 1296, 1331, 1372, 1458, 1500, 1715, 1728, 1875, 1944, 2000, 2048, 2058, 2187, 2197, 2250, 2401, 2500
OFFSET
1,1
COMMENTS
Numbers k such that P(k)^3 | k, where P(k) = A006530(k).
Numbers k such that A071178(k) >= 3.
LINKS
EXAMPLE
8 is a term since 2^3|8 and 2 is the largest prime factor of 8.
54 = 2*3^3 is a term since 3^3|8 and 3 is the largest prime factor of 54.
MATHEMATICA
Select[Range[2500], FactorInteger[#][[-1, 2]] > 2 &]
PROG
(Python)
from sympy import factorint
def c(n, e): f = factorint(n); return f[max(f)] >= e
def ok(n): return n > 1 and c(n, 3)
print([k for k in range(2501) if ok(k)]) # Michael S. Branicky, May 30 2022
CROSSREFS
Subsequence of A070003.
Subsequences: A036966 \ {1}, A349306 \ {1}, A354562.
Sequence in context: A059172 A360558 A107606 * A349306 A245713 A320966
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 30 2022
STATUS
approved